In Search of Continuity: Thoughts of an Epistemic Empiricist by Ian Durham

Ian,

Just so! Despite Kuhn's wider popularity, I was always more drawn to Popper's rejection of all forms of historicism (Kuhn, Hegel/Marx, etc.) in favor of the progressive model of critical rationalism (although I admit my personal philosophy is more rational idealist).

Anyway, when you spoke of "hopping sideways" among points, it struck a chord, because a week or so ago I happened to be thumbing through an old copy on my bookshelf of Roscza Petr's book on infinity. One of the illustrations had to do with mapping a discrete point to every locus of another independent set of points -- possible only if the point is of sufficient distance from the other set. Because we assume that there are no such isolated points in our universe, your "hopping" model would be the only physical way to connect all the dots (so to speak). For this reason, I think if quantum field theory is to succeed, it will have to be topological (Witten) where distance has a different meaning. More insight in my essay, if you get a chance.

Tom

complementarity

Ok, what "complementarity principle"?

Bohr Complementarity

Dear Ian,

thanks for spelling my name correctly, and not with swapped doubles, as many people in your continent do.

I am afraid I still don't see your point. Perhaps the source of confusion is in the idea of trying to bring around the x-axis and t-axis on a discrete structure exactly as one would do on a continuous manifold. (I do understand that you are not the one who wants to do this!) This is inappropriate. On a causal set (our discrete structure) one cannot rely on cartesian axes for obtaining the space and time values of an event. So, it is true, as you wrote, that x and t are not defined in between the points, BUT they are not even defined *on* the points: if one insists for having definite (x, t) coordinates for an event, he should embed the whole causal set in a manifold, and read out the coordinates from the latter. These would be coordinates relative to a specific reference frame. But one of the nice features of causal sets is that they describe the pure causal structure of events while abstracting from any specific embedding/frame, in the same way as Lorentz distance is invariant for all inertial observers.

So I still do not see why it should be easier to be trapped in the erroneous belief that information might hop from point to point, and event 'sideways', w.r.t. a discrete structure, than to be trapped in the analogous error w.r.t. a continuous structure, picturing information jumping outside the light cone.

But, as I said, this was really a minor point. Thanks for the pointer to Hawking and Sachs. I have one for you, if you are interested: a one-page discussion of causal sets by R. Sorkin. My essay is in line with those basic ideas, but departs from them in the causet growth dynamics, which in my approach is algorithmic and fully deterministic.

Tommaso

Dear T H Ray,

The own page that you link says at the very start "This article needs attention from an expert on the subject".

The literature about Bohr's complementarity principle that I know is rather ambiguous and often completely incorrect.

It must be emphasized that the standard formulation of QM is based in a set of postulates, none of which is a "complementarity principle".

It's hardly worth a debate. Complementarity is now part of the history of quantum theory and was never (unlike uncertainty and nonlocality) an essential feature.

Tom

Dear Readers,

There are three kinds of the essays in our contest: 1) the essays with original physics research where all physics' information was created by their authors. Often such essays seem to have errors because they often contradict orthodox theory. 2) There are essays-stories about physics which contain generally known physics' information copied from the textbooks or papers and author's commentaries (for example Jarmo Makela, Singh, Durham, Funakoshi and so on). Such essays have ARTISTIC VALUE only but not scientific value; usually these essays-stories do not have any errors by definition because all physics' information was copied from the textbooks and other published papers. 3) There are essays of mixed type containing mixed information. It is clear that the authors of the essays-stories have advantages because their essays never contain errors since all Physics' information was copied from the textbooks.

What kind of the essay must FQXi community support? If we support the essays-stories, we'll transform FQXi into the entertainment community. For example, instead of my ''interpretation of quantum mechanics'' I could send the jokes about Bohr, Einstein or stories like Gamov's ''Mr. Tompkins in paperback''. It would be very interesting and fun. Another option is to create artistic essays-discussions with Einstein, Bohr, or Aristotle following the example of Jarmo Makela. In this context, the next logical step is to organize a banquet for the authors of essays where we tell jokes and funny stories about physics. What is our purpose?

Since the goals of the FQXi (the "Contest") are to: Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology; Identify and reward top thinkers in foundational questions, therefore I ask readers to vote for essays with original research rather than for essays-stories. In this way we'll encourage the fundamental physics research but not entertainment essays.

Sincerely,

Constantin

Dear T H Ray,

Effectively, there is not such *principle* in quantum mechanics, but found only in early debates (e.g. Bohr vs Einstein) during the development of quantum mechanics, when many stuff was novel and not still understood.

However, Lawrence B Crowell wrote on Feb. 27, 2011 @ 00:26 GMT,

"The relationship between the continuous and discrete aspects of the world seems to be an example of a complementary principle."

He does not seem to be considering the historical roots of quantum mechanics, but some essential feature of the world, which I see nowhere. Therein my (still unanswered) question to him: what principle?

Dear Constantin Zaharia Leshan,

I sympathize with your views.

I only want to remark two things. The first, that it is not true that the "essays-stories" do not have any errors because were copied from textbooks and papers. I have given some examples of the contrary both in the forums and in my own Essay.

The second, that I do not consider Singh' Essay to be only of artistic value (see my 'review' of it as well!).

I wrote in the above post about the PHYSICAL information and physical laws. Your argument about radar guns is not about PHYSICS; For example, the uncertainty principle is a physical information but not guns, cars, ships and so on - It's about technology.

Your essay use generally known physics information that was NOT created by you. Therefore it is true that the essay contain physical information copied from the textbooks and Internet. I understand that really you learned all this information at the University and then you prepared your essay using your memory. However, it is the same - your essay contains GENERALLY KNOWN PHYSICAL INFORMATION copied from external sources.

For example, infnitesimal changes, parabolic functions, Zeno's paradox, Doppler effect, Spekkens' epistemic interpretation of quantum mechanics - it is generally known information copied from textbooks. If you comments about quantum mechanics and SR it does not means that it is YOUR information: ''Quantum field theory combines quantum mechanics with special relativity and so technically deals with a at (Euclidean) spacetime". You are NOT the creator of this physical information. The essays filled with such information and authors commentaries is not original and contains information copied from general sources as textbooks, papers, Internet and so on.

Please show me the PHYSICAL information created by YOU in your essay.

Also, I don't see any proofs in your essay that the Universe is digital or analog. The discussions about radar guns prove nothing about reality.

Constantin

Dear Juan R. González-Álvarez,

Thank you for support. In my view, the FQXi prize deserves the people who really are able to create PHYSICS; the prize is not for writers and copiers.

There are a lot of the essays and I do not have time to analyze all. Nevertheless, I'll analyze the Singh' Essay more carefully.

Regards,

Constantin

I must agree with Constantin Leshan: if, indeed, FQXI intends

"to catalyze, support, and disseminate research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality but unlikely to be supported by conventional funding sources"

the mission which requires a *very rear* kind of expertise, especially now when our overloaded schedules meet with the absolutely unprecedented in the history of science transitional period. This very rear expertise should be found and used effectively. Otherwise, the mission will not be believable, and, which is more, will only *undermine* the future similar undertakings.

I'm sorry, I mistyped: of course I meant "very rare" rather than "very rear" ;-))

Gentleman,

My essay deals with nothing but foundations, and so I can understand your frustration, but if you have an axe to grind you should take it up with FQXI not Dr. Durham!

Robert

Dear Constantin,

The FQXi is the "Foundational" Questions Institute. The idea is to probe the foundations of pre-existing theories, perhaps propose modifications to these foundations, or even (if absolutely necessary) to propose entirely new foundations. But really, proposing ENTIRELY NEW, completely original physics should be a last resort. I can think of no example where this method has been fruitful in the past. Take the discovery of special relativity, for example. There is a case in which the equations (the Lorentz transformations) were already "in the textbooks". Einstein reinterpreted them, employing a foundational analysis. Would you accuse Einstein of plagiarising here? An equation on its own doesn't tell us much. We need to know what it could mean. There are, in physics, usually (most probably always) multiple options in how we understand the mapping between equations and reality.

Your request for statements that "prove something about reality" must be, in the end, a request for a foundational (or interpretive) analysis (and an epistemological one at that). The point of many of these competitions (and the submissions) has been to probe just what can be said about reality GIVEN OUR THEORIES. You may think you are being a hard-nosed scientist, a la Feynman or Pauli perhaps, but you are in fact just espousing a very naive philosophical position. Feynman and Pauli might have spoken in a similar way, but their actual work revealed a very different, more sophisticated philosophical understanding.

Finally, I have to agree with Robert Spoljaric that your beef ought to be with FQXi.

Best,

Dean

Robert,

It goes without saying that my remark has nothing to do with Ian.

[ First, my apologies to Ian for 'using' his page. However, who knows, there might be some benefits to FQXi ;-) ]

"But really, proposing ENTIRELY NEW, completely original physics should be a last resort. I can think of no example where this method has been fruitful in the past."

Dear Dean,

The whole point is this: Can the development of physics continue successfully along the path similar to its historic past, or we reached the point of 'no return', when we simply have to begin anew? It appears that FQXi should allow for the latter to be at least one of the main possibilities. By the way, a number of physicists, including Lee Smolin, do believe in such possibility.

There are also a number of philosophers who firmly believe in that possibility.